There is known a drive system for a hybrid vehicle, which is provided with an engine, an electric motor, and a clutch disposed in a power transmitting path between the engine and the electric motor. In the field of such type of hybrid vehicle drive system, there has been proposed a technique to switch a drive mode on the basis of an operation amount of an accelerator pedal, between an engine drive mode in which the engine is placed in its operated state while the clutch is placed in its engaged state, and a motor drive mode in which the electric motor is exclusively used as a drive power source while the engine is placed in its rest state and while the clutch is placed in its released state. Patent Document 1 discloses an example of such a drive mode switching control device for a hybrid vehicle.